We have the following integral:
$$\int_0^1 \frac{P_3(t)}{\sqrt{1-k^2 P_3^2(t)}}dt$$
where $P_3(t)$ is a third-degree polynomial with all coefficients different from zero.
Is it an elliptic integral?
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My professor gave us this question on a calculus II quiz. One of my calculus III pals suggested I use surface integrals, but that tool is not available to us (I don't know how to use it yet, nor do my ...

Given that $ e= \frac{a^2-b^2}{b^2} $ , and $L$ is the length of the perimeter, which equals $4aE(e, \pi/2)$, find the length of the perimeter up to $e^2$ in terms of $a$ and $b$.
How does one begin ...

Can someone please explain how Fricke and Klein obtain the integral relationa stated at the top of p. 34 in this book? The entire book can be previewed on Google Books. It is an old book and I do not ...

Is there any way to evaluate
$$\int^{x_2} _{x_1} \sqrt{(a - b x^m)}~ dx $$
where $x_{12} = \pm (a/b)^{1/m}$
without elliptic functions or hypergeometry? Or just any way to solve it. My attempt is to ...

I need to find the area enclosed by the ellipse $b^2x^2 + a^2y^2=a^2b^2$, and I know it involves taking the integral, but I'm not sure what function I should be taking the integral of or how to find ...

I'm reading a paper on the Schwarz D minimal surface, and I'm wondering whether the authors have made a mistake. They evaluate the integral
$$
\int_0^z \frac{2t\;\mathrm{d}t}{\sqrt{t^8-14t^2+1}},
$$
...

The Wikipedia articles on elliptic integral and elliptic functions state that “elliptic functions were discovered as inverse functions of elliptic integrals.” Some elliptic functions have names and ...

So, I've got a real doozy of a question. I'm trying to provide a proof for the relationship between the major and minor radius ($a$ and $b$, respectively) of an ellipse of constant circumference as ...

During some electromagnetics calculation regarding a loop antenna I stumbled across the following integral
$$\int_0^{\pi/2} \frac{d\phi}{\big(1+\frac{k}{k-2}\cos(2\phi)\big)^{3/2}}$$
and Mathematica ...

I read the section about Abel's theorem and the Jacobi Inversion Problem on the book of Forster, "Lectures on Riemann Surfaces".
I would like if there were some books which treats more in detail this ...

I am trying to compute the Complete elliptical integral of second kind kind in Mathematica with Parameter m=-19.7 .Following is the response from Mathematica.
Input:EllipticE[-19.71]
Output:4.81841
...

While trying to prove that $$(1)\qquad x\sum_{k=0}^\infty\frac{2^{-5k}(6k+1)((2k-1)!!)^3}{4(k!)^3} = 1 \implies x=\pi$$
I got to a point, using W|A, where I have to prove that $$\color{red}{(2)\qquad ...